Linear Optimization with Box Constraints in Banach Spaces

K. C. Sivakumar () and J. M. Swarna
Additional contact information
K. C. Sivakumar: Indian Institute of Technology Madras
J. M. Swarna: Anna University

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 2, No 9, 377-387

Abstract: Abstract Let X be a partially ordered real Banach space, let a,b∈X with a≤b. Let φ be a bounded linear functional on X. We say that X satisfies the box-optimization property (or X is a BOP space) if the box-constrained linear program: max 〈φ,x〉, s.t. a≤x≤b, has an optimal solution for any φ,a and b. Such problems arise naturally in solving a class of problems known as interval linear programs. BOP spaces were introduced (in a different language) and systematically studied in the first author’s doctoral thesis. In this paper, we identify new classes of Banach spaces that are BOP spaces. We present also sufficient conditions under which answers are in the affirmative for the following questions: (i) When is a closed subspace of a BOP space a BOP space? (ii) When is the range of a bounded linear map a BOP space? (iii) Is the quotient space of a BOP space a BOP space?

Keywords: Partially-ordered Banach spaces; Box optimization spaces (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-008-9481-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9481-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-008-9481-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().